具有遗漏故障的最优最终拜占庭协议
Optimal Eventual Byzantine Agreement Protocols with Omission Failures
AI总结：
针对遗漏故障，提出基于知识的最优最终拜占庭协议程序，分离信息交换与行动协议，实现高效且最优的FIP，解决开放问题。
摘要：
关于最优最终拜占庭协议（EBA）的研究——这些协议在精确意义上，在每次运行中尽可能快地做出决定，并保证所有无故障代理决定相同的值——一直集中于全信息协议（FIP），其中代理反复向其他每个代理发送完全描述其过去观察结果的消息。虽然可以证明，在不失一般性的情况下，我们可以将最优协议视为FIP，但由于所需的消息大小，全信息交换对于许多应用来说不切实际。我们将协议分为两部分：信息交换协议和行动协议，以便能够检查更有限的信息交换的影响。然后，我们定义了相对于信息交换协议的最优性概念。粗略地说，行动协议P相对于信息交换协议E是最优的，如果在使用P时，代理在按照E交换信息的行动协议中尽可能快地做出决定。我们提出了一个针对遗漏故障的基于知识的EBA程序，其所有实现都保证正确，并且如果信息交换满足某种安全条件，则这些实现是最优的。然后，我们在两个感兴趣的环境中构建了实现该基于知识的程序的具体程序，并证明这些环境满足安全条件。最后，我们表明，对我们程序的一个小修改产生了一个既最优又可高效实现的FIP，解决了Halpern、Moses和Waarts（SIAM J. Comput.，2001）提出的一个开放问题。
英文摘要：
Work on \emph{optimal} protocols for \emph{Eventual Byzantine Agreement} (EBA) -- protocols that, in a precise sense, decide as soon as possible in every run and guarantee that all nonfaulty agents decide on the same value -- has focused on emph{full-information protocols} (FIPs), where agents repeatedly send messages that completely describe their past observations to every other agent. While it can be shown that, without loss of generality, we can take an optimal protocol to be an FIP, full information exchange is impractical to implement for many applications due to the required message size. We separate protocols into two parts, the \emph{information-exchange protocol} and the \emph{action protocol}, so as to be able to examine the effects of more limited information exchange. We then define a notion of optimality with respect to an information-exchange protocol. Roughly speaking, an action protocol $P$ is optimal with respect to an information-exchange protocol $\mathcal{E}$ if, with $P$, agents decide as soon as possible among action protocols that exchange information according to $\mathcal{E}$. We present a knowledge-based EBA program for omission failures all of whose implementations are guaranteed to be correct and are optimal if the information exchange satisfies a certain safety condition. We then construct concrete programs that implement this knowledge-based program in two settings of interest that are shown to satisfy the safety condition. Finally, we show that a small modification of our program results in an FIP that is both optimal and efficiently implementable, settling an open problem posed by Halpern, Moses, and Waarts (SIAM J. Comput., 2001).
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